As far as I understand, Let’s Encrypt SSL certs work just like any other paid SSL certs. If you are not facing any problems with common SSL cert, you will not face any problems with Let’s Encrypt. But if ~1 minute of downtime is acceptable for your website, I think it would be better to use --standalone option to obtain certificate to not let Let’s Encrypt touch your configs. Also Let’s Encrypt nginx plugin is still in beta, and you will not be able to install it with letsencrypt-auto at this moment.

UPDATE: If you are using EasyEngine v3.4+ then you can configure letsencrypt certificate with one command. Please check the Let’s Encrypt Command. First make sure that your site is live and running on same server on which you are running Let’s...